Question

Solve 3(x+2)=5x+3-2x=3 . Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice

1. x = _______
2. The equation has infinitely many solutions.
3.The equation has no solution.

Answer 1

Upon simplifying the given equation, we reach a contradiction (6 = 3), which indicates that there are no solutions to the equation. The correct choice is therefore that the equation has no solution.

Step-by-step explanation:

We have the equation 3(x + 2) = 5x + 3 - 2x. Let's solve it step by step.

1. Firstly, distribute the 3 on the left side: 3x + 6 = 5x + 3 - 2x.
2. Now, combine like terms on the right: 3x + 6 = 3x + 3.
3. Subtract 3x from both sides of the equation: 6 = 3.

We have reached a false statement, which means that the equation has no solution. There's no value for x that would satisfy the original equation. Therefore, the correct choice is option 3.